The present invention relates to a vector controlling method and apparatus for an induction motor, and more particularly, to a vector controlling method and apparatus for an induction motor which does not require a speed detector.
An induction motor is most widely used as a power source for various mechanisms and apparatuses in industrial fields. This is because the induction motor has peculiar advantages in that it has a simple structure, needs little maintenance and exhibits excellent durability and low production costs.
The induction motor is, however, very difficult to control because the dynamic characteristic thereof is clearly nonlinear, with many interactive variables present. Much investigation into techniques of controlling the induction motor for high performance has been widely carried out. In the 1980s, with the advent of the rapid development of semiconductors, complicated control theories were applied to actual systems to further advance induction motor control techniques. Especially, the vector control method developed in the early 1970s provided for the characteristics of the induction motor to be divided into a magnetic flux component and a torque component, so that the induction motor could be controlled with the high performance of a direct-current motor, which greatly broadened the scope of application of induction motors. However, the vector controlling method needs data on the angular velocity of a rotator and therefore requires a speed detector such as a tachogenerator and encoder. This complicates a system, deteriorates the durability and reliability of the induction motor, destabilizes the system, and increases production cost.
A method of detecting the magnetic flux of a rotator has been proposed by Ohtani in a paper entitled "Vector Control of Induction Motor without Shaft Encoder" (IEEE Transactions on Industry Application, Vol. 28, No. 1, January/February, 1992). This method will be explained below.
Provided that the d axis of the d-q coordinates rotating at the angular velocity (electrical angular velocity .omega.) of induction motor coincides with the magnetic flux vector of the rotator, the relationship between the magnetic flux .phi..sub.r of rotator, generated torque T.sub.e and the angular velocity .omega..sub.r of induction motor can be expressed as follows. ##EQU1## where M is mutual inductance; I.sub.d1 is the d-axis component (magnetic flux component) of the primary-side (stator) current; I.sub.q1 is the q-axis component (torque component) of the primary-side (stator) current; T.sub.2 is a time constant (L.sub.2 /R.sub.2) of the secondary-side (rotator); L.sub.2 is rotator inductance; R.sub.2 is rotator resistance; and P is an operator (d/dr) for differentiation.
In other words, the generated torque T.sub.e and angular velocity .omega..sub.r of an induction motor are determined by magnetic flux vector .phi..sub.r of the rotator and primary-side currents I.sub.d1 and I.sub.q1. The generated torque and torque-component current, i.e., the main control variables, can be given as the following equations (4.1) and (5.1) on the orthogonal coordinates (.alpha.-.beta.) fixed coordinates or x-y fixed coordinates) of the stator. ##EQU2## where .phi..sub..alpha. =.phi..sub.r cos(.omega.t+.rho.); .phi..sub..beta. =.phi..sub.r sin(.omega.t+.rho.); i.sub..alpha. =I.sub.1 cos(.omega.t+.gamma.*+.rho.); and i.sub..beta. =I.sub.1 sin(.omega.t+.gamma.*+.rho.).
Assuming that .rho. is the angle of the d axis with respect to the .alpha. axis when t=0 (and may be given as zero), then .gamma.* and I.sub.1 can be expressed as follows. EQU .gamma.*=tan.sup.-1 (I.sub.q1 /I.sub.d1) EQU I.sub.1 =(I.sub.d1.sup.2 +I.sub.q1.sup.2).sup.1/2
The calculation equation for the rotator magnetic flux, used by Ohtani, is as follows. ##EQU3## where V.sub..alpha. and V.sub..beta. are stator voltages on .alpha. and .beta.; i.sub..alpha. and i.sub..beta. are stator currents on .alpha. and .beta.; R.sub.1 is the primary-side stator resistance; L.sub.rl.alpha. and L.sub.rl.beta. are the total leakage inductance on .alpha. and .beta. or L.sub.1 (1-M.sup.2 /L.sub.1 L.sub.2); and L.sub.1 is the primary-side stator reactance.
FIG. 1 is a block diagram of the rotator magnetic flux calculator proposed by Ohtani.
Referring to FIG. 1, the calculator comprises a current-controlled inverter 1, an induction motor 2, a subtractor 3, a multiplier 4 having the variable value of R.sub.1 +L.sub.rl P, an integration circuit 5 having the characteristic value of ##EQU4## an integration circuit 7 having the characteristic value of ##EQU5## and an adder 6.
A rotator induction voltage e is applied to integration circuit 5, and the magnetic flux command .phi.* of rotator is applied to integration circuit 7. The outputs of integration circuits 5 and 7 are summed to detect the rotator magnetic flux.
The output e of subtractor 3 is expressed as the following equation (8.1). EQU e=V.sub.1 +(R.sub.1 +l.sub.p)i.sub.1 ( 8.1)
where V.sub.1 =V.sub..alpha. +jV.sub..beta. and i.sub.1 =i.sub..alpha. +ji.sub..beta..
Therefore, equations (6.1) and (7.1) are expressed as the following equation (9.1). ##EQU6## where .phi.*=.phi..sub..alpha. +j.phi..sub..beta..
As shown in equations (6.1) and (7.1), Ohtani's method of calculating the magnetic flux of rotator requires integration. In implementing the method, if a pure integrator is used and a direct-current offset or drift is present in the input value, the calculated value of the magnetic flux diverges and is rather unreliable. For this reason, Ohtani instead used a lag circuit similar to the integrator. In low-speed operation, however, the calculation value of the lag circuit is considerably different from the actual value and interferes with the rotator speed so that a complete vector control is impossible. In Ohtani's method, the problem was solved by inhibiting the control of magnetic flux at low speeds. This solution is imperfect for enabling a proper vector control throughout the speed ranges.
Further, the Ohtani method needs additional external hardware such as an accelerator for initially driving the motor, because the calculated value of the rotator magnetic flux is unstable in initial driving.